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An effective variational iteration algorithm for solving Riccati differential equations. (English) Zbl 1192.65095
Summary: The piecewise variational iteration method (VIM) for solving Riccati differential equations (RDEs) provides a solution as a sequence of iterates. Therefore, its application to RDEs leads to the calculation of terms that are not needed and more time is consumed in repeated calculations for series solutions. In order to overcome these shortcomings, we propose an easy-to-use piecewise-truncated VIM algorithm for solving the RDEs. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the classical fourth-order Runge-Kutta method (RK4) verify that the new method is very effective and convenient for solving Riccati differential equations.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
65L06Multistep, Runge-Kutta, and extrapolation methods
Full Text: DOI
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